Modeling coskewness with zero correlation and correlation with zero coskewness
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916529502683136 |
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| author | Bernard, Carole Chen, Jinghui Vanduffel, Steven |
| author_facet | Bernard, Carole Chen, Jinghui Vanduffel, Steven |
| contents | This paper shows that one needs to be careful when making statements on potential links between correlation and coskewness. Specifically, we first show that, on the one hand, it is possible to observe any possible values of coskewness among symmetric random variables but zero pairwise correlations of these variables. On the other hand, it is also possible to have zero coskewness and any level of correlation. Second, we generalize this result to the case of arbitrary marginal distributions showing the absence of a general link between rank correlation and standardized rank coskewness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modeling coskewness with zero correlation and correlation with zero coskewness Bernard, Carole Chen, Jinghui Vanduffel, Steven Probability Theoretical Economics Statistics Theory This paper shows that one needs to be careful when making statements on potential links between correlation and coskewness. Specifically, we first show that, on the one hand, it is possible to observe any possible values of coskewness among symmetric random variables but zero pairwise correlations of these variables. On the other hand, it is also possible to have zero coskewness and any level of correlation. Second, we generalize this result to the case of arbitrary marginal distributions showing the absence of a general link between rank correlation and standardized rank coskewness. |
| title | Modeling coskewness with zero correlation and correlation with zero coskewness |
| topic | Probability Theoretical Economics Statistics Theory |
| url | https://arxiv.org/abs/2412.13362 |